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% %% Jose Antonio Abell Mena provided this for DSL descriptions
% % (used in a file _Chapter_SoftwareHardware_Domain_Specific_Language_English.tex
% % This is added for listing FEI DSL
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% \usetheme{Singapore} % ima sadrzaj i tackice gore
% \usetheme{Antibes} % ima sadrzaj gore i kao graf ...
% \usetheme{Berkeley} % ima sadrzaj desno
% \usetheme{Berlin} % ima sadrzaj gore i tackice
% \usetheme{Goettingen} % ima sadrzxaj za desne strane
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%%%%%%%
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%%%% HYPERREF HYPERREF HYPERREF HYPERREF HYPERREF
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% \usepackage[pdfauthor={Boris Jeremic},
% colorlinks=true,
% linkcolor=webblue,
% citecolor=webblue,
% urlcolor=webblue,
% linktocpage,
% pdftex]{hyperref}
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% or whatever
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% does not look nice, try deleting the line with the fontenc.
% Site Specific Dynamics of Structures:
%From Seismic Source to
%the Safety of Occupants and Content
\title[RealESSI]
{Nuclear Installation Lifecycle: \\
Modeling and Simulation of \\
Design Basis and Beyond Design Basis \\
ESSI Behavior
}
%\subtitle
%{Include Only If Paper Has a Subtitle}
%\author[Author, Another] % (optional, use only with lots of authors)
%{F.~Author\inst{1} \and S.~Another\inst{2}}
%  Give the names in the same order as the appear in the paper.
%  Use the \inst{?} command only if the authors have different
% affiliation.
\pgfdeclareimage[height=0.2cm]{universitylogo}{/home/jeremic/BG/amblemi/ucdavis_logo_blue_sm}
\pgfdeclareimage[height=0.7cm]{lbnllogo}{/home/jeremic/BG/amblemi/lbnllogo}
\author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Yuang Feng, Han Yang, Hexiang Wang, Fangbo Wang, \\
\vspace*{2mm}
Boris Jeremi{\'c}
}
%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
\institute[\pgfuseimage{universitylogo}\hspace*{0.1truecm}\pgfuseimage{lbnllogo}] % (optional, but mostly needed)
%{ Professor, University of California, Davis\\
{ University of California, Davis, CA\\
% and\\
% Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
Lawrence Berkeley National Laboratory, Berkeley, CA}
%  Use the \inst command only if there are several affiliations.
%  Keep it simple, no one is interested in your street address.
\date[] % (optional, should be abbreviation of conference name)
{\small SMiRT25\\
Charlotte, NC, USA, August 2019}
\subject{}
% This is only inserted into the PDF information catalog. Can be left
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% If you have a file called "universitylogofilename.xxx", where xxx
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%\pgfdeclareimage[height=0.2cm]{universitylogo}{/home/jeremic/BG/amblemi/ucdavis_logo_gold_lrg}
%\logo{\pgfuseimage{universitylogo}}
% \pgfdeclareimage[height=0.5cm]{universitylogo}{universitylogofilename}
% \logo{\pgfuseimage{universitylogo}}
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{
\begin{scriptsize}
\begin{frame}
\frametitle{Outline}
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% \tableofcontents[currentsection]
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\end{scriptsize}
}
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\titlepage
\end{frame}
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\begin{frame}
\frametitle{Outline}
\begin{scriptsize}
\tableofcontents
% You might wish to add the option [pausesections]
\end{scriptsize}
\end{frame}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Structuring a talk is a difficult task and the following structure
% may not be suitable. Here are some rules that apply for this
% solution:
%  Exactly two or three sections (other than the summary).
%  At *most* three subsections per section.
%  Talk about 30s to 2min per frame. So there should be between about
% 15 and 30 frames, all told.
%  A conference audience is likely to know very little of what you
% are going to talk about. So *simplify*!
%  In a 20min talk, getting the main ideas across is hard
% enough. Leave out details, even if it means being less precise than
% you think necessary.
%  If you omit details that are vital to the proof/implementation,
% just say so once. Everybody will be happy with that.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Introduction}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{\ }
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Motivation}
\begin{itemize}
%\vspace*{0.3cm}
\item[] Improve modeling and simulation for infrastructure objects
\vspace*{2mm}
\item[] Expert numerical modeling and simulation tool
% \vspace*{1mm}
% \item[] Use of numerical models to
% analyze statics and dynamics of soil/rockstructure systems
%
\vspace*{2mm}
\item[] Control and reduce modeling uncertainty
%\vspace*{1mm}
% \item[] Choice of analysis level of sophistication
\vspace*{2mm}
\item[] Goal: Predict and Inform rather than fit
\vspace*{2mm}
\item[] Engineer needs to know!
%
%
%
% \vspace*{1mm}
% \item[] Follow the flow, input and dissipation, of seismic energy,
\vspace*{2mm}
\item[] System for modeling and simulation of
Earthquakes and/or Soils and/or Structures and their Interaction:\\
RealESSI,
\vspace*{2mm}
% % \hspace*{25mm}
{ \bf \url{http://realessi.info/} }
% % \hspace*{25mm}
% \url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}{{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
% % \url{http://msessi.info/}
%
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Prediction under Uncertainty}
\begin{itemize}
%\vspace*{1mm}
\item \underline{Modeling Uncertainty}, Simplifying assumptions
\begin{itemize}
\vspace*{2mm}
\item[] Low, medium, high sophistication modeling and simulation
\vspace*{2mm}
\item[] Choice of sophistication level for confidence in results
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\vspace*{4mm}
\item \underline{Parametric Uncertainty}, ${M} \ddot{u_i} + {C} \dot{u_i} + {K}^{ep} {u_i} = {F(t)}$,
\begin{itemize}
\vspace*{2mm}
\item[] Uncertain mass $M$, viscous damping $C$ and stiffness $K^{ep}$
\vspace*{2mm}
\item[] Propagation of uncertainty in loads, $F(t)$
\vspace*{2mm}
\item[] Results are PDFs and CDFs for $\sigma_{ij}$, $\epsilon_{ij}$, $u_i$, $\dot{u}_i$, $\ddot{u}_i$
\end{itemize}
\end{itemize}
%
%
% %Le doute n'est pas un {\'e}tat bien agr{\'e}able,\\
% mais l'assurance est un {\'e}tat ridicule. (Fran{\c c}oisMarie Arouet, Voltaire)
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{Modeling Uncertainty}
\begin{itemize}
\item[] Important (?!) features are simplified, 1C vs 3C, inelasticity
%\vspace*{4mm}
% \item Unrealistic and unnecessary modeling simplifications
\vspace*{1mm}
\item[] Modeling simplifications are justifiable if one or two
level higher sophistication model demonstrates that features being
simplified out are not important
\end{itemize}
% local
%\vspace*{2mm}
\begin{center}
\hspace*{7mm}
%\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
\movie[label=show3,width=5.5cm,poster,autostart, showcontrols]
{\includegraphics[width=50mm]
{/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_2_npps_mp4_icon.jpeg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_2_npps.mp4}
%
%\hfill
\hspace*{5mm}
%
\movie[label=show3,width=6.0cm,poster,autostart,showcontrols]
{\includegraphics[width=50mm]
{/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
{/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
\hspace*{7mm}
%\end{flushleft}
%%
\end{center}
% local
% % \vspace*{5mm}
% \begin{center}
% %\begin{flushleft}
% % \hspace*{15mm}
% \movie[label=show3,width=5cm,poster,autostart,showcontrols]
% {\includegraphics[width=5cm]
% {/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
% {/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
% %\end{flushleft}
% %%
% \hfill
% %%
% %\begin{flushright}
% % \hspace*{15mm}
% \movie[label=show3,width=5cm,poster,autostart,showcontrols]
% {\includegraphics[width=5cm]
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation_screen_grab.jpg}}
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
% %\end{flushright}
% \end{center}
%
\end{frame}
%OVDE
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Modeling Uncertainty, 6C vs 1C Motions}
%
%
% % local
% \vspace*{2mm}
% \begin{center}
% \hspace*{7mm}
% %\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% \movie[label=show3,width=8.8cm,poster, showcontrols]
% {\includegraphics[width=92mm]
% {/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_2_npps_mp4_icon.jpeg}}
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/movie_2_npps.mp4}
% \end{center}
% % local
% % \vspace*{2mm}
% % \begin{center}
% % \hspace*{7mm}
% % \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% % {\includegraphics[width=90mm]{movie_2_npps_mp4_icon.jpeg}}{movie_2_npps.mp4}
% % \end{center}
%
%
% % online
% \vspace*{12mm}
% \begin{flushleft}
% %\vspace*{15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4}
% {\tiny (MP4)}
% \end{flushleft}
% % online
%
%
%
%
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Parametric Uncertainty: Soil Stiffness and Strength}
\vspace*{2mm}
%\vspace*{3mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{7mm}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01Ed.pdf}
\hspace*{3mm}
% \hfill
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/YoungModulus_Histogram_Normal_01Ed.pdf}
%
\end{center}
\end{figure}
\vspace*{5mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{7mm}
\includegraphics[width=5.00truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/ShearStrength_RawData_and_MeanTrendMod.pdf}
\hspace*{3mm}
% \hfill
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/ShearStrength_Histogram_PearsonIVFineTunedMod.pdf}
%
\end{center}
\end{figure}
%\vspace*{5mm}
%\vspace*{1.8cm}
%\hspace*{3.3cm}
\begin{flushright}
{\tiny
(cf. Phoon and Kulhawy (1999B))\\
~}
\end{flushright}
%
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Parametric Uncertainty: Material Properties}
%
%
%
% \vspace*{5mm}
% \begin{figure}[!hbpt]
% \begin{center}
% % %
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiPdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiCdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuPdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuCdf.pdf}
% \\
% %\vspace*{2mm}
% \hspace*{2.5cm} \mbox{\tiny Field $\phi$} \hspace*{3.5cm} \mbox{\tiny Field $c_u$}
% \\
% \vspace*{10mm}
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiPdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiCdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuPdf.pdf}
% \hspace*{3mm}
% \includegraphics[width=2.5truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuCdf.pdf}
% \\
% %\vspace*{8mm}
% \hspace*{2.5cm} \mbox{\tiny Lab $\phi$} \hspace*{3.5cm} \mbox{\tiny Lab $c_u$}
% \end{center}
% \end{figure}
%
%
%
% \end{frame}
%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{RealESSI Simulator System}
%
% The RealESSI,
% {\underline {\bf Real}}istic
% %{\underline {\bf M}}odeling and
% %{\underline {\bf S}}imulation of
% {M}odeling and
% {S}imulation of
% {\underline {\bf E}}arthquakes,
% {\underline {\bf S}}oils,
% {\underline {\bf S}}tructures and their
% {\underline {\bf I}}nteraction. Simulator is a software, hardware and
% documentation system for time domain,
% linear and nonlinear, inelastic, deterministic or probabilistic, 3D, finite
% element modeling and simulation of:
%
% \begin{itemize}
% %\vspace*{1mm}
% \item statics and dynamics of soil,
% %\vspace*{1mm}
% \item statics and dynamics of rock,
% %\vspace*{1mm}
% \item statics and dynamics of structures,
% %\vspace*{1mm}
% \item statics of soilstructure systems, and
% %\vspace*{1mm}
% \item dynamics of earthquakesoilstructure system interaction
% \end{itemize}
%
%
%
% Used for:
% \begin{itemize}
% %\vspace*{1mm}
% \item Design, linear elastic, load combinations, dimensioning
%
%
% %\vspace*{1mm}
% \item Assessment, nonlinear/inelastic, safety margins
% \end{itemize}
%
%
%
%
% \end{frame}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{RealESSI Simulator System}
%
%
% \begin{itemize}
%
%
% \item RealESSI System Components
% \begin{itemize}
% \item RealESSI Preprocessor (gmsh/gmESSI, X2ESSI)
% \item RealESSI Program (local, remote, cloud)
% \item RealESSI PostProcessor (Paraview, Python, Matlab)
%
% \end{itemize}
%
% \vspace*{1mm}
% \item RealESSI System availability:
% \begin{itemize}
% %\vspace*{1mm}
% \item Educational Institutions: Amazon Web Services (AWS), free
% \item Government Agencies, National Labs: AWS GovCloud
% \item Professional Practice: AWS, commercial
% %\vspace*{1mm}
% %%\vspace*{1mm}
% % \item Sources available to collaborators
% \end{itemize}
%
%
%
% \vspace*{1mm}
% \item RealESSI Short Courses, online, worldwide
%
%
%
% \vspace*{1mm}
% \item System description and documentation at
% \url{http://sokocalo.engr.ucdavis.edu/~jeremic/Real_ESSI_Simulator/}
% %
% %\url{http://realessi.info/}
% %
%
%
% % \vspace*{2mm}
% % \item
% %
%
%
% \end{itemize}
%
%
% \end{frame}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Modeling and Simulation of ESSI for Nuclear Installations}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{\ }
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Regional Geophysical Models}
\begin{itemize}
\item Free Field seismic motions on regional scale
\vspace*{4mm}
\item Knowledge of geology (deep and shallow) needed
\vspace*{4mm}
\item Developed using SW4 and/or RealESSI
\vspace*{4mm}
\item Collaboration with LLNL: Dr.~Rodgers, Dr.~Pitarka and Dr.~Petersson
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Regional Geophysical Models}
\begin{figure}[!htb]
\begin{center}
\includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/San_Francisco__Regional_Model_BIG.jpg}
\includegraphics[width=5.2truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/San_Francisco__Regional_Model.jpg}
\end{center}
% \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
\end{figure}
Rodgers and Pitarka
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Regional Geophysical Models}
\begin{figure}[!htb]
\begin{center}
\includegraphics[width=10truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/USGBay_Area_Model_CC_det2_sm.jpg}
\end{center}
% \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
\end{figure}
USGS
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Example Regional Model}
%
% \begin{figure}[!htb]
% \begin{center}
% \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Vs_at_top.jpg}
% % \includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Horizontal_Velocity_at_12s.jpg}
% \includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Peak_Velocity.jpg}
% \end{center}
% % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
% \end{figure}
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Example Regional Model (Rodgers)}
%\vspace*{5mm}
\begin{center}
%\hspace*{5mm}
%
%\movie[label=show3,width=10.0cm,poster,autostart,showcontrols]
\movie[label=show3,width=8.0cm,poster]
%\movie[label=show3,width=6.0cm,poster,showcontrols]
{\includegraphics[width=80mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/M6_5_s500_BASIN_STOCHASTIC_mag_SLOW.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/M6_5_s500_BASIN_STOCHASTIC_mag_SLOW.mpg}
\hspace*{5mm}
%
\end{center}
% online
\vspace*{5mm}
\begin{flushleft}
\hspace*{5mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/M6_5_s500_BASIN_STOCHASTIC_mag_SLOW.mpg}
{\tiny (MP4)}
%\hspace*{5mm}
\end{flushleft}
% online
% out
% out %\vspace*{2mm}
% out \begin{center}
% out \hspace*{15mm}
% out %
% out \movie[label=show3,width=8.0cm,poster,autostart,showcontrols]
% out {\includegraphics[width=60mm]{BJicon.png}}{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/M6.5_s500_BASIN+STOCHASTIC.mag.SLOW.mpg}
% out \hspace*{15mm}
% out %
% out \end{center}
% out
% out
% out \begin{flushleft}
% out \vspace*{15mm}
% out \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Rodgers_Free_Field_motions/M6.5_s500_BASIN+STOCHASTIC.mag.SLOW.mpg}
% out % \href{./homo_50mmesh_45degree_Ormsby.mp4}
% out {\tiny (MP4)}
% out \end{flushleft}
% out %
% out
\end{frame}
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\begin{frame}
\frametitle{Energy Input and Dissipation}
\begin{itemize}
\vspace*{1mm}
\item[] Energy input, dynamic forcing
\vspace*{4mm}
\item[] Energy dissipation outside SSI domain:
\begin{itemize}
\item[] SSI system oscillation radiation
\item[] Reflected wave radiation
\end{itemize}
%\vspace*{1mm}
\item[] Energy dissipation/conversion inside SSI domain:
\begin{itemize}
\item[] Inelasticity of soil, contact zone, structure, foundation, dissipators
\item[] Viscous coupling with internal/pore fluids, and external fluids
% % \item[] potential and kinetic energy
% \item[] potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
\end{itemize}
%\vspace*{1mm}
% \item[] Numerical energy dissipation (numerical damping/production and period errors)
% \item[] Numerical energy dissipation (damping/production)
\item[] Numerical energy dissipation/production
\end{itemize}
%
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Plastic Energy Dissipation}
\vspace*{2mm}
Single elasticplastic element under cyclic shear loading
\begin{itemize}
\item[] Difference between plastic work and plastic dissipation
\item[] Plastic work can decrease
\item[] Plastic dissipation always increases
\end{itemize}
%\vspace*{7mm}
\begin{figure}[!hbpt]
\begin{center}
\hspace*{5mm}
\includegraphics[width=11.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Dissipation_Material.png}
\end{center}
\end{figure}
\end{frame}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Energy Dissipation Control Mechanisms}
%
% \begin{figure}[!H]
% %\hspace*{10mm}
% \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_plasticity.pdf}
% \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Rayleigh.pdf}
% \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Newmark.pdf}
% \end{figure}
%
%
% % \hspace*{10mm} Numerical \hspace*{20mm} Viscous \hspace*{20mm} Plasticity
% \hspace*{10mm} Plasticity \hspace*{20mm} Viscous \hspace*{20mm} Numerical
%
%
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Energy Dissipation Control}
\begin{figure}[!H]
%\hspace*{10mm}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_a.pdf}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_b.pdf}
\includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_g.pdf}
% \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_e.pdf}
\end{figure}
\end{frame}
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%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{Inelastic Modeling of Soil Structure Systems}
\begin{itemize}
%\vspace*{1mm}
\item Soil, inelastic, elasticplastic
\begin{itemize}
\item[] Dry, single phase
\item[] Unsaturated, partially saturated
\item[] Fully saturated
\end{itemize}
%\vspace*{1mm}
\item Contact, inelastic, soil/rock  foundation
\begin{itemize}
\item[] Dry, single phase,
\begin{itemize}
\item[] Normal, hard and soft, gap open/close
\item[] Friction, nonlinear
\end{itemize}
\item[] Fully saturated, suction, excess pressure, buoyant force
\end{itemize}
%\vspace*{1mm}
\item Structure, inelastic, damage, cracks
\begin{itemize}
\item[] Nonlinear/inelastic 1D reinforced concrete fiber beam
\item[] Nonlinear/inelastic 3D reinforced concrete solid element
\item[] Alcali Silica Reaction concrete modeling
\end{itemize}
%%\vspace*{1mm}
% \item FluidSolid interaction (open surface)
\end{itemize}
%
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{NPP Model }
%
% \begin{figure}[!h]
% \begin{center}
% \includegraphics[width=8.5cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/NPP_With_Shallow_Foundation.pdf}
% \end{center}
% % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
% \end{figure}
%
%
% % \begin{tikzpicture}[remember picture,overlay]
% % \node[xshift=3.5cm,yshift=0.6cm] at (current page.center) {\includegraphics[width=0.5\textwidth]{images/Contact_In_Industry}};
% % \end{tikzpicture}
%
% \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Structure Model}
%
% The nuclear power plant structure comprise of
% \begin{itemize}
% \item Auxiliary building, $f^{aux}_{1}= 8Hz$
% \item Containment/Shield building, $f^{cont}_{1}= 4Hz$
% \item Concrete raft foundation: $3.5m$ thick
% \end{itemize}
% \begin{figure}[!h]
% \begin{center}
% \includegraphics[width=0.8\textwidth]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/NPP_Model_Auxiliary_And_Containment_Building.pdf}
% \end{center}
% \caption{\label{Fig:NPP_Structure_Model_In_Real_ESSI} Auxiliary and Containment Building }
% \end{figure}
%
% \end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Inelastic Soil and Inelastic Contact}
\begin{itemize}
\item Shear velocity of soil $V_s=500m/s$
\item Undrained shear strength (Dickenson 1994) $V_s [m/s] = 23 (S_u [kPa])^{0.475}$
\item For $V_s=500m/s$ Undrained Strength $S_u=650kPa$ and Young's Modulus of $E=1.3GPa$
\item von Mises, Armstrong Frederick kinematic hardening
($S_u=650kPa$ at $\gamma=0.01\%$; $h_a = 30MPa$, $c_r = 25$)
\item Soft contact (concretesoil), gaping and nonlinear shear
\end{itemize}
\begin{figure}[!h]
\begin{center}
\includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Von_Mies_non_Linear_Hardening.pdf}
\includegraphics[width=3.5cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/SoftContact.pdf}
\end{center}
\end{figure}
\end{frame}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Acc. Response, Top of Containment Building}
%
% \begin{figure}[!h]
% \begin{center}
% \hspace*{8mm}
% \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_X.pdf}
% \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_Y.pdf}
% \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_Z.pdf}
% \\
% \hspace*{8mm}
% \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_X.pdf}
% \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_Y.pdf}
% \includegraphics[width=3.54cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_Z.pdf}
% % \caption{\label{Fig:Response_of_Top_of_Containment_Building} Seismic Response at Top of Containment Building}
% \end{center}
% \end{figure}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Acceleration Traces, Elastic vs Inelastic }
\hspace*{35mm}
\begin{figure}[!h]
\vspace*{2mm}
\begin{center}
\hspace*{15mm}
\includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Acceleration_Elastic_Without_Contact_SMIRT_2017.pdf}
\hspace*{20mm}
\includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Acceleration_Inelastic_With_Contact_SMIRT_2017.pdf}
\hspace*{25mm}
\end{center}
\end{figure}
\hspace*{35mm}
\hspace*{10mm} Elastic \hspace*{40mm} Inelastic \hspace*{40mm}
\end{frame}
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\begin{frame}
\frametitle{Displacement Traces, Elastic vs Inelastic}
\hspace*{35mm}
\begin{figure}[!h]
\vspace*{2mm}
\begin{center}
\hspace*{15mm}
\includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Elastic_Without_Contact_SMIRT_2017.pdf}
\hspace*{20mm}
\includegraphics[width=7.0cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Inelastic_With_Contact_SMIRT_2017.pdf}
\hspace*{25mm}
\end{center}
\end{figure}
\hspace*{35mm}
\hspace*{10mm} Elastic \hspace*{40mm} Inelastic \hspace*{40mm}
\end{frame}
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\begin{frame}
\frametitle{Energy Dissipation in a LargeScale Model}
% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy
% \vspace*{5mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
{/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
\end{center}
\begin{flushleft}
\vspace*{15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation.mp4}
% \href{./homo_50mmesh_45degree_Ormsby.mp4}
{\tiny (MP4)}
\end{flushleft}
%
\end{frame}
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\begin{frame}
\frametitle{Uncertainty Propagation through
Inelastic System}
%
\begin{itemize}
\item Incremental elpl constitutive equation
%
\begin{eqnarray}
\nonumber
\Delta \sigma_{ij}
=
% E^{EP}_{ijkl}
E^{EP}_{ijkl} \; \Delta \epsilon_{kl}
=
\left[
E^{el}_{ijkl}

\frac{\displaystyle E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}}
{\displaystyle n_{rs} E^{el}_{rstu} m_{tu}  \xi_* h_*}
\right]
\Delta \epsilon_{kl}
\end{eqnarray}
\vspace*{3mm}
\item Dynamic Finite Elements
%
\begin{equation}
{ M} \ddot{ u_i} +
{ C} \dot{ u_i} +
{ K}^{ep} { u_i} =
{ F(t)}
\nonumber
\end{equation}
\vspace*{3mm}
\item Material and load parameters are uncertain
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Probabilistic ElasticPlastic Modeling}
% % \vspace*{5mm}
% \begin{center}
% % \hspace*{15mm}
% \movie[label=show3,width=7cm,poster,autostart,showcontrols]
% {\includegraphics[width=7cm]
% {/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_Plastic_Dissipation_Density.png}}
% %{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_without_Contact_vonMises.mp4}
% {NPP_without_Contact_vonMises.mp4}
% \end{center}
%\vspace*{5mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=9cm,poster,autostart,showcontrols]
{\includegraphics[width=9cm]
{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.png}}
% /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
%{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Animations/PEP_Animation.mp4}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/PEP_Animation.mp4}
\end{center}
%
% \includegraphics[width = 12cm]{./img/figure_PEP_25.pdf}
\end{frame}
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%\section[Formulation]{Stochastic Dynamic Finite Element Formulation}
%\subsection[Time domain stochastic Galerkin method]{Time domain stochastic Galerkin method}
%\frame{\tableofcontents[currentsubsection,sectionstyle=show/shaded]}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{Stochastic ElasticPlastic Finite Element Method}
\begin{itemize}
\item Material uncertainty expanded into stochastic shape funcs.
%$E(x,t,\theta) = \sum_{i=0}^{P_d} r_i(x,t) * \Phi_i[\{\xi_1, ..., \xi_m\}]$
\vspace*{1mm}
\item Loading uncertainty expanded into stochastic shape funcs.
%$f(x,t,\theta) = \sum_{i=0}^{P_f} f_i(x,t) * \zeta_i[\{\xi_{m+1}, ..., \xi_f]$
\vspace*{1mm}
\item Displacement expanded into stochastic shape funcs.
%$u(x,t,\theta) = \sum_{i=0}^{P_u} u_i(x,t) * \Psi_i[\{\xi_1, ..., \xi_m, \xi_{m+1}, ..., \xi_f\}]$
%\item
%Stochastic system of equation resulting from Galerkin approach (static example):
%
%\item Time domain integration using Newmark and/or HHT, in probabilistic spaces
\end{itemize}
\begin{tiny}
\[
%$
\begin{bmatrix}
\sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_0> K^{(k)} & \dots & \sum_{k=0}^{P_d} <\Phi_k \Psi_P \Psi_0> K^{(k)}\\
\sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_1> K^{(k)} & \dots & \sum_{k=0}^{P_d} <\Phi_k \Psi_P \Psi_1> K^{(k)}\\ \\
\vdots & \vdots & \vdots & \vdots\\
\sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_P> K^{(k)} & \dots & \sum_{k=0}^{M} <\Phi_k \Psi_P \Psi_P> K^{(k)}
\end{bmatrix}
\begin{bmatrix}
\Delta u_{10} \\
\vdots \\
\Delta u_{N0}\\
\vdots \\
\Delta u_{1P_u}\\
\vdots \\
\Delta u_{NP_u}
\end{bmatrix}
=
%\]
%\[
\begin{bmatrix}
\sum_{i=0}^{P_f} f_i <\Psi_0\zeta_i> \\
\sum_{i=0}^{P_f} f_i <\Psi_1\zeta_i> \\
\sum_{i=0}^{P_f} f_i <\Psi_2\zeta_i> \\
\vdots \\
\sum_{i=0}^{P_f} f_i <\Psi_{P_u}\zeta_i>\\
\end{bmatrix}
%$
\]
\end{tiny}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{SEPFEM: System Size}
\begin{itemize}
\item SEPFEM offers a complete solution (single step)
\vspace*{2mm}
\item It is NOT based on Monte Carlo approach
\vspace*{2mm}
\item System of equations does grow (!)
\end{itemize}
\vspace*{4mm}
% \normalsize{Typical number of terms required for a SEPFEM problem} \vspace{1cm}\\
\scalebox{0.7}{
\begin{tabular}{ c c c c}
\# KL terms material & \# KL terms load & PC order displacement& Total \# terms per DoF\\ \hline
4 & 4 & 10 & 43,758 \\
4 & 4 & 20 & 3,108,105 \\
4 & 4 & 30 & 48,903,492 \\
6 & 6 & 10 & 646,646 \\
6 & 6 & 20 & 225,792,840 \\
% 6 & 6 & 30 & 1.1058 $10^{10}$ \\
% 8 & 8 & 10 & 5 311 735 \\
% 8 & 8 & 20 & 7.3079 $10^{9}$ \\
% 8 & 8 & 30 & 9.9149 $10^{11}$\\
... & ... & ... & ...\\
% \hline
\end{tabular}}
\end{frame}
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\begin{frame}
\frametitle{SEPFEM: Example in 1D}
\vspace*{2mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=9cm,poster,autostart,showcontrols]
{\includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_elastic_900.png}}
% /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
%{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Animations/SEPFEM_Animation_Elastic.mp4}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Probabilistic_Elasto_Plasticity_and_Stochastic_Elastic_Plastic_Finite_Element_Method/SEPFEM_Animation_Elastic.mp4}
\end{center}
% \includegraphics[width = 12cm]{./img/figure_elastic_900.pdf}
\end{frame}
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\section{Conclusion}
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\subsection{\ }
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\begin{frame}
\frametitle{Summary}
\begin{itemize}
\vspace*{2mm}
\item Numerical modeling to predict and inform, rather than fit
\vspace*{4mm}
\item Engineer needs to know
\vspace*{4mm}
\item Model, simulate and understand full life cycle of an object
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% \item Education and Training is the key!
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\item Funding from and collaboration with the USDOE, USNRC, USNSF,
USBR, USFEMA CNSCCCSN, UNIAEA, and Shimizu Corp. is greatly appreciated,
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\item More info: \hspace*{3mm} {\bf \url{http://realessi.info/}}
\end{itemize}
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